Psychological and Physiological Acoustics (others): Paper ICA2016-625

Modelling of the auditory ribbon

Pablo Etchemendy(a), Ramiro Vergara(a) and Manuel Eguía(a)

(a)Laboratorio de Acústica y Percepción Sonora, Departamento de Ciencias Sociales, Universidad Nacional de Quilmes, B1876BXD, Bernal, Bs. As., Argentina. [email protected]

Abstract The coding of the fine temporal details of auditory stimuli by the auditory system is required for many auditory tasks. For instance, the temporal information conveys information necessary for the perception of pitch and for the angular localization of sound sources. The first stage where this kind of information is processed is the auditory periphery. Inside the periphery, the (RS) of auditory inner hair cells excels for its temporal acuity, a fact that has driven many recent physiological and computational studies. In this work we present a biophysical model of the auditory Ribbon Synapse (RS) of inner hair cells, which contains many anatomical details obtained from the electrophysiological data available in the literature, and is able to reproduce known features of the RS, namely, temporal adaptation of due to partial vesicular depletion and gradual increment of the exocytosis rate as the membrane is depolarized. We used the model to study some aspects that are difficult to tackle experimentally, in particular, the influence of a vesicular fusion step on: (a) the formation of a “ring-like” spatial pattern of exocitosis, compatible with the spatial structure of postsynaptic receptors; and (b) the degree of synchronization of exocytosis as a function of release event size. The results described could be relevant in order to improve our knowledge of the temporal coding of auditory stimuli at the auditory periphery level. Keywords: auditory periphery, ribbon synapse, temporal coding, computational modelling, inner Modelling of the auditory ribbon synapse

1 Introduction The auditory system excels at temporal processing tasks. Acoustic source localization, pitch perception, speech recognition and source separation, among other functions, rely on the pre- cise coding of temporal features in the range between tens of microseconds and a few mil- liseconds. In order to achieve this formidable task, the auditory system has developed several specialized mechanisms in the periphery and the first stages of neural processing. A promi- nent and widely studied structure among them is the synapse between the Inner Hair Cells (IHC) and the auditory nerve afferent fibers (spiral cells). This is the first synapse in the auditory system and is the responsible of transducing the graded potential of the IHC (in response to the basilar membrane displacements) into all-or-none events at the postsynaptic nerve fibers. This synapse bears a highly advanced and specialized structure, the synaptic ribbon, that many studies have spotted as the main responsible of completing the demanding signalling task: the sustained release with high reliability, low latency and min- imum variability. This structure positions a great amount of synaptic vesicles close to release sites, within nanometers of calcium channels and directly across from postsynaptic glutamate receptors, in the so-called “”. Whenever a basilar membrane displacement depolar- izes the IHC the opening probability of the calcium channels increases. It has been shown that the opening of a single in the active zone can trigger the vesicle release (ex- ocytosis) and a postsynaptic . Also, individual ribbons are capable of sustaining exocytosis at several hundreds of vesicles per second without fatigue, which is in turn reflected in rates of action potentials in individual auditory nerve fibers of hundred of hertz. Despite its phenomenal and well studied capabilities (see [1, 2] for review), a complete picture of the machinery of the ribbon synapse is still missing and many fundamental questions about its underlying mechanisms remain unanswered. For example, individual postsynaptic potentials vary in amplitude, suggesting multiquantal release of vesicles, either by homotypic fusion before exocytosis, or by synchronous exocytosis of multiple vesicles docked beneath the ribbon. Yet, a recent work has questioned the multiquantal release proposing an alternative mechanism [3]. Thus, the origin and possible roles of are still unclear. Also, several works have confirmed that the distribution of postsynaptic receptors displays a ring-like shape [4, 5]. Since a great part of the outstanding characteristics of the synaptic ribbon comes from its precise co-localization with presynaptic channels, it is reasonable to hypothesize that this ring-like distribution could be related to the spatial distribution of vesicle release. In this work we advance in a dynamical, yet simplified and hopefully accurate biophysical model of the auditory ribbon synapse, that could give some insight into the underlying mechanisms of this complex structure. Models are useful not only for interpreting and understanding ex- perimental results but also for testing alternative hypothesis, and for selection an planning of new experiments, as long as the models have some predictive power. Previous models of the whole ribbon synapse have been proposed either as phenomenological [6] or minimal theoreti- cal descriptions [7], and there is only one work that develops a detailed biophysical description

2 of the structure [8]. However this last model does not incorporate the multivesicular release. We will develop an experimentally constrained biophysical model focusing on the spatial and timing characteristics of the ribbon synapse and the possible roles of multivesicular release. Hence we will model in detail the spatial distribution and time events of channels and vesicles, resigning other not less important features as calcium diffusion and buffering and kinetics of calcium sensors.

2 Description of the model The main feature of the model is the description of the ribbon synapse from a spatial point of view. The synaptic ribbon is represented as a two-dimensional, square grid in which tethered vesicles are able to diffuse freely (Fig. 1). The mapping of the synaptic ribbon’s spheroidal surface to a square allows to capture one important aspect of this structure: the ribbon is believed to act as a vesicle trap, reducing the dimension of the space available for diffusion and thus helping vesicles to reach the active zone [9, 10]. Each site of the grid can be empty or filled by a single vesicle. The ribbon is divided in two regions. Sites located at three sites or less from the center define the active zone (AZ), which corresponds to the lower region of the ribbon. Vesicles located at the active zone are in contact with the plasmalemma, and near to voltage-gated CaV1.3 calcium channels located within the plasma membrane [11]. In hair cells, these channels are colocalized with the synaptic body [12], which facilitates the interaction between the entering Ca2+ and the neighboring vesicles exocytic sensors. In the model, a total of 80 calcium channels [13] are located within a 4.5-sites radius from the AZ center. The middle and upper regions of the ribbon are represented by the remaining sites. Vesicles can enter the ribbon through a simple refilling process, controlled by the probability per free site and per time unit that a free vesicle gets tethered to the ribbon. Only sites outside the active zone can accept new vesicles and the process is unidirectional; vesicles can abandon the ribbon only through exocytosis. The combination of refilling, diffusion and exocytosis processes allows to model the continuous activity of the auditory synaptic ribbon, and therefore investigate aspects related to the reliable transmission of long-lasting auditory stimuli. In the rest of this section we will describe the details of the model and its implementation. In Table 1 we list the model parameters along with the references from the literature used to set their values. The model was implemented in Matlab 2013. Calcium channels dynamic was solved using Gillespie’s “direct method” [14], with an upper limit for the sampled time to next reaction set to 0.01 ms for variable inputs.

2.1 Anatomic aspects The grid has a size of 13×13 sites, thus having a total of 169 sites. The active zone (AZ) is defined by a circle of radius RAZ equal to 3 sites, which gives a total of 29 sites. These figures are between the values reviewed by Nouvian et al. [15] for the ribbon-associated vesicles at the mouse IHC (125 to 200 vesicles, depending on the microscopy method) and for the docked vesicles at the AZ (16 to 30 vesicles). Each site can be considered as having a size of 40×40

3 Figure 1: (a) Schematic of the anatomy of the synapse. The elements included in the model are the synaptic ribbon, the synaptic vesicles and the calcium channels located at the cellular membrane. (b) Spatial grid describing the synapse. The legend on the right shows the correspondence between anatomy and model.

nm, thus representing a 20-nm radius vesicle [16]. The total number of calcium channels (NCC) is the mean number of ribbon-associated calcium channels considering all in the entire cell [13]. We assumed a uniform distribution of channels inside a circle of radius RCC located at the base of the synaptic body, concentric with the active zone; in each simulation channel locations were sampled at time zero and then remained constant. RCC was set to 4.5 sites, a value a little greater than RAZ, which guarantees that inner and outer sites of the active zone are surrounded by the same number of channels in average.

2.2 Dynamic of calcium channels and exocytosis mechanism Each calcium channel is stochastically modelled by a simple two-state scheme:

α O )−−−−* C (1) β where O represents the “open” state and C the “closed” state. Transitions between states are governed by the voltage-dependent rates α(V) (opening) and β(V) (closing):

h h −1 α(V) = α0 · (V −Vα ) · (1 − exp((Vα −V)/kα )) , h −1 (2) β(V) = β0 − β1 · (1 + exp((V −Vβ )/kβ )) , Parameter values were obtained by fitting the experimental data referred by Wittig and Parsons [8]. The resulting open probability for an ensemble of channels increases as the membrane is depolarized, from a near-zero value for V near to −80 mV to a maximum of 0.4 for V greater than −10 mV, in concordance with other data available in the literature [13]. Exocytosis is governed by the interaction between Ca2+ ions and a Ca2+ sensor located within each vesicle. A detailed representation of this step thus requires the modelling of the calcium concentration along the AZ (which can display sharp variations in short distances, see [8, 17]); and of the internal state of the sensor associated with each vesicle. In order to simplify our description of the synapse, we assumed a “nanodomain” model for exocytosis, following the

4 Table 1: Summary of parameters and their corresponding references from the literature.

Parameter Symbol Value Reference Half-side of the grid L 6.5 sites Nouvian et al. [15] Active zone radius R 3 sites Anatomy of the synapse AZ Channels region radius RCC 4.5 sites See sec. 2.1 Number of channels NCC 80 Brandt et al. [13] −1 −1 α0 0.129 ms mV Opening rate α(V) κα 7.6 mV h Vα −38.4 mV −1 −1 Calcium channels dynamics β0 12.5 ms mV β 9.35 ms−1 mV−1 Wittig & Parsons [8] Closing rate β(V) 1 κβ 13.3 mV h Vβ 0.9 mV Radius threshold r 20 nm Exocytosis ex Temporal threshold tex 1 ms Diffusion coefficient D 50 nm2 ms−1 Chapochnikov et al. [3] Vesicular dynamics −1 Refilling rate per site ρr 0.039 ms Goutman [19] Vesicular fusion Degree of fusion γ(V) See sec. 2.4 Glowatzki & Fuchs [20]

proposal that the stochastic gating of one or few channels is sufficient to trigger the release of nearby vesicles [1, 2, 13]. The model obeys the following rule: every time a calcium channel re- mains opens a time tex or more, all vesicles within a distance rex from the channel are released. Parameters tex and rex were set following Wittig and Parsons [8]. These authors calculated the detailed interaction between the calcium concentration and the accepted model of the calcium sensor [18] for clusters of vesicles located at the active zone. Considering a depolarization to −20 mV, they found that: (a) a group of 10 to 30 vesicles takes between 0.75 and 1 ms for the release of the first vesicle (first latency); and (b) released vesicles are overlapped with the calcium channels. Therefore, we set tex to 1 ms and rex to 20 nm. This simple implementa- tion allowed us to capture the basic aspects of a nanodomain-coupling scheme, while saving computational cost and reducing the complexity of the model.

2.3 Vesicular diffusion and refilling In our model, every single vesicle attached to the synaptic ribbon is free to diffuse to any empty neighboring site located at the same row or column (i.e., to any first-neighboring site). The probability per time unit for the occurrence of such event was adjusted in a way such that the coefficient of diffusion of a single vesicle in an empty ribbon was 50 nm2 ms−1, following [3]. The refilling process is controlled by the probability per free site and per time unit (ρr) for a free site to be occupied by a new vesicle. As we stated earlier, only sites not belonging to the active zone can accept new vesicles. The active zone recovers only through diffusion from the medium and upper regions of the ribbon. This induces a bi-exponential law of recovery in the absence of exocytosis, as the recovery process also depends on the coefficient of diffusion. We adjusted ρr in a way that the fast time constant of the process was 37 ms, following the experimental results of Goutman [19].

5 2.4 Vesicular fusion step The last aspect of the model is an instantaneous vesicular fusion step that triggers each time a vesicle undergoes exocytosis (as described in sec. 2.2). Vesicles located at first-neighboring sites can be fused with the originating vesicle following the probability rule given by ps(V) = exp(−s2/γ(V)), with s set to 1, where γ(V) is a function of the V that controls the degree of fusion (larger γ implies lesser ps). This rule is applied in successive steps considering the occupied first-neighboring sites of the vesicles added in the previous step, until no vesicles are added. In each step s increases by one unit; this guarantees an asymptotic value of 0 for ps. The function γ(V) was defined following the distribution of EPSC sizes obtained by Glowatzki and Fuchs [20]. The key aspect of the EPSC distribution is that it remains unchanged for different depolarization conditions. We fitted γ(V) in order to obtain a mean release size of 4.3 vesicles in the physiological range of potentials, considering a summing window of 2 ms (this accounts for the rise and decay time of the EPSC measured by Glowatzki and Fuchs, which was in the range 1-3 ms). The resulting γ(V) decreases as the membrane potential increases, in an inverse fashion to the open probability. In other words, the model requires the increase of ps in order to maintain constant the mean number of vesicles per release event as the cell is depolarized.

3 Results 3.1 Spatial pattern of exocytosis We studied the spatial pattern of exocytosis under different conditions of depolarization (six conditions, from −80 to −20 mV) and degree of fusion (two conditions: activated and deac- tivated). We tracked the positions at which release events occurred, and then counted the number of events and of released vesicles. In Fig. 2a we show the resulting spatial maps of exocytosis for six representative cases. The color code is relative to each plot: blue indicates zero activity, and red indicates the maximum value of each condition; in this way we can eas- ily inspect each pattern regardless of absolute values. The amount of neurotransmitter (NT) displays a clear ring-like pattern for V equal to or greater than 50 mV and activated fusion, with the majority of exocytosis occurring at the border of the active zone, while almost none in its center. The number of events shows a similar pattern, although weaker, when considering equal conditions. Finally, for deactivated fusion, we observe lesser differences between inner and outer regions, and little variations with depolarization level. In order to better quantify these findings we collapsed the data to the radial axis. To this end we averaged the values between sites located at the same distance from the center. Fig. 2b shows the curves corresponding to each condition. In the presence of vesicular fusion, the increase in activity from center to border can be as big as 8x for the released NT (consider −30 mV). On the other hand, in the absence of vesicular fusion, the increase is 0.6x at most (consider same potential). Increment values, defined as xborder/xcenter − 1, are shown at the rightmost part of each curve. Increments are greater in the presence of fusion than in its absence, and under vesicular fusion they are greater for the NT than for the number of events.

6 Figure 2: (a) Spatial maps of release at the AZ, for different membrane potentials. Color code is relative to the maximum value obtained in each condition, in order to better visu- alize variations. (b) Radial curves summarizing spatial data for all conditions. Each curve is labelled by the center-to-border proportional increment (see text). For both (a) and (b) upper and middle rows indicate event and neurotransmitter (NT) release, respectively, in the presence of vesicular fusion. Lower row indicates the same in the absence of fusion.

3.2 Synchronization and multiquantal release We studied the response of the model to oscillations of the membrane potential with the form:

V(t) = 0.5 · (V1 +V2) − 0.5 · (V1 −V2) · sin(2π f0t) (3) with V1 set to −80 mV; V2 between −60 and −20 mV; and f0 between 125 and 4000 Hz. These values of V1 and V2 are similar to the physiological values in response to an acoustic stimuli of moderate intensity. We analyzed the results by means of the synchronization index (SI) which measures the degree of coupling of the response to a certain phase of the stimulus [21]. Fig. 3 shows SI for each condition (blue markers). The main feature to note is the increase of SI with V2. We also note a slight dependence of SI with frequency, which is more noticeable as V2 increases. In order to study the effect of the fusion step on SI, we segregated the events of ex- ocytosis in two groups, using as criteria the median event size: “big” events (size greater than 5 vesicles) and “small” (size less than 6 vesicles). We found that SI for the big-events group is consistently greater than for the small-events group, and that the difference between them increases as V2 decreases (see Fig. 3, green and red markers). Finally, we analyzed changes

7 V = −60 mV V = −50 mV V = −40 mV V = −30 mV V = −20 mV 2 2 2 2 2 0.8

0.6

S. I. All 0.4 Big Small

0.2 125 250 500 1k 2k 4k 125 250 500 1k 2k 4k 125 250 500 1k 2k 4k 125 250 500 1k 2k 4k 125 250 500 1k 2k 4k Freq. [Hz] Freq. [Hz] Freq. [Hz] Freq. [Hz] Freq. [Hz]

Figure 3: Synchronization (SI) as a function of stimulus frequency for different values of V2 (see Eq. 3). Data is also segregated according to event size as described in text. in SI in the absence of the fusion step and found that SI remains practically unchanged (differ- ences smaller than 2%) with respect to the all-events SI obtained in its presence.

4 Final remarks Our results reveal aspects that could be relevant to the understanding of the temporal pro- cessing at the auditory ribbon synapse. Both results are in line with previously reported data obtained in electrophysiological and anatomical studies, as we will see below. The spatial pattern of release correlates with the ring-like density of postsynaptic AMPA re- ceptors found in previous studies in rats and mice [4, 5]. In our model, exocytic events occur mostly at the border of the active zone, and this pattern is enhanced when depolarization increases and vesicular fusion is present. The main feature described by our model of the synapse is the fact that vesicles approach the active zone from its border due to the impen- etrability of the synaptic ribbon. Vesicles are more likely to reach the center when the open probability of calcium channels is low. Therefore, it is reasonable to expect a more uniform spatial pattern when the cell is weakly depolarized than when it is not, as can be seen in Fig. 2. The fusion step enhances the pattern as fusion causes more depletion at the active zone compared with the no-fusion condition (data not shown); thus vesicles are more likely located at its border than at its center. Regardless of whether vesicular fusion occurs at the ribbon synapse, our results suggest an association between synapse anatomy and response. Our re- sults point to the synaptic ribbon as a necessary element that brings compatibility between the pre and postsynaptic structures, as it causes the majority of neurotransmitter to be released at the closest possible distance to the postsynaptic receptors, which could serve as a booster for the generation of action potentials. When considering oscillating stimuli (the kind of stimuli the IHC is intended to process), we found that larger release events are better synchronized with the stimuli than smaller events in the presence of vesicular fusion. This finding held for different levels of depolarization and stimulus frequency, indicating a possible advantage of such a mechanism, as larger events are more likely to induce fast and large postsynaptic action potentials. These results correlate with

8 the finding that multiquantal EPSC events are better phase-locked than small evoked EPSCs in adult bullfrogs [22]. Interestingly, the effect was more prominent for weak stimuli, which could be useful to increase the chance of preserving temporal information for weak stimuli. Future studies need to address whether the described features of the presynaptic response could affect the postsynaptic latency, jitter and synchronization. A spatial model of the synaptic cleft and postsynaptic receptors could be a natural extension of our model and serve as basis for the study of glutamate release, diffusion and interaction with the cluster of AMPA receptors.

Acknowledgements This work was funded by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) of Argentina and Universidad Nacional de Quilmes. References

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